Yes, there is no evidence that vinegar treats genital warts, either. That's kind of a myth that started with doctors using a weak acidic solution to identify warts (that doesn't really work either) and that led to people using different types of vinegar to treat them.
Really, your best bet is to just go to the doctor.
That's not how a person would get cancer. The only real concern here is the potential for infection. The best steps you can take are keeping the area clean and dry, and don't keep examining or touching it, as you'll aggravate the wound and potentially introduce bacteria. https://intermountainhealthcare.org/services/wound-care/wound-care/conditions/chemical-wounds/
Also, you should see a doctor about genital warts. Home remedies have a high instance of failure, and as you have learned, can cause damage.
There is no evidence that applying vinegar, topically, leads to cancer of any kind.